Summary: By using the critical point theory, the existence of periodic solutions for \(2n\)th-order nonlinear \(p\)-Laplacian difference equations is obtained. The main approaches used in our paper are variational techniques and the saddle point theorem. The problem is to solve the existence of periodic solutions for 2\(n\)th-order \(p\)-Laplacian difference equations. The results obtained successfully generalize and complement the existing ones.